I've noticed that many of the wide angle prime lenses (at least for Canon) have somewhat smaller apertures than their normal or telephoto counterparts. E.g. the regular Canon 24mm prime is f/2.8 while the 50mm prime is f/1.8.

Theoretically, it should be possible to make large aperture wide angle lenses, as their opening will be much smaller than primes with longer focal lengths. So, why are there no wide angle lenses with larger apertures? Does a larger aperture place limits on the smallest aperture a lens can have, as this could have an impact on the depth of field for landscape photography.

I would think it's because while it is probably possible to make a large-aperture wide-angle lens, it's more or less unnecessary to go to the expense of doing so. Wide angle lenses are landscape lenses, and the situations are few where you want less than 4 feet of sharpness in a landscape shot.
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ElendilTheTallNov 24 '11 at 9:55

@ElendilTheTall At wide angles your depth of field is huge at all reasonable focus distances, so that's not the reason for the lack of fast wide angle lenses. For example if you had a 14mm f/1.4 on full frame and focused it more than 15 feet away, your depth of field would be measured in miles not feet!
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Matt GrumNov 24 '11 at 12:16

3 Answers
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Broadly speaking wide aperture lenses are easier to design the longer the focal length. The reason that you don't see any 400mm f/1.4 lenses is due to manufacturing difficulties, e.g. keeping dispersion low while producing elements of the size required for such apertures. It's worth restating that the designation f/1.4 means that the size of the aperture stop is the focal length divided by 1.4, which for a 400 f/1.4 is a whopping 285mm. Technically it's the image of the aperture stop that must be that size, which means the front element has to be at least that big.

If you look at the widest of Canon's superteles you see a pattern that 150mm seems to be about the limit of what is economical:

400/2.8 = 142mm

600/4.0 = 150mm

800/5.6 = 142mm

Lenses with focal length less that the registration distance (about 46mm for most DSLRs) have to incorporate what's known as a retrofocal design, which is essentially a reverse telephoto group (or "wide converter") at the back of the lens. The wider the lens the more corrections have to be performed due to the retrofocal design, and these corrections are more difficult for wide apertures lenses.

You can see this if you look at the design of the Canon 24mm f/2.8 and 50mm f/1.8:

Canon 24mm f/2.8

50mm f/1.8

The reason 50mm offer such good price/performance ratio when it comes to aperture is that for 35mm cameras that 50mm sits at the sweet spot where the focal length is long enough to allow a simpler non retrofocal design, but not too long that large pieces of glass have to be used to give a good f/number.

Supplemental: in addition to solving the mechanical problem (rear-element-to-film-plane distance), retrofocals also produce a larger image circle for a given focal length. True wide-angle lenses usually require a degrading filter (a graduated ND filter that's denser at the centre than at the edges) to bring vignetting down to an acceptable level at wider apertures. That would mean that your lens might have an f-stop of, say, 1.4, but a t-stop of 2.8 with the filter in place, for no net gain. And you'd have to change filters when you change apertures.
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user2719Nov 24 '11 at 22:59

Modern wide angle lenses are in effect reverse telephotos. So there's a lot of glass even if the focal length is smaller. In addition, the amount of glass needed to correct abberations is larger than in a lens with normal focal length.

Canon does have both a 28mm f/2.8 and a 28mm f/1.8 lens. According to this table (PDF) the f/2.8 is a 5 group 5 lens construction, while the f/1.8 is a 9 group 10 lens construction. So you have nearly doubled the number of glass elements while opening up a bit more than 1 stop, and 28mm isn't very extreme wideangle.

The wide aperture does not have an effect on the smallest aperture. There may be a mechanical issue in that you won't get a very accurate f/32 on an extreme wideangle, due to the shape of the aperture blades.

Also, while a smaller aperture will increase the apparent depth of field, you will lose sharpness due to diffraction. Search around this site for that topic for more information!

Making a fast lens it's not just a matter of making "a bigger hole". The lens needs to "bend" the light to cover the whole frame, and the more extreme the bending (as in wide angle) the greater the aberrations...